Yes, the Economy 7 tariff is so named for the 7 hours of cheap rate juice each night. It normally runs midnight-7am when were on GMT, 1-8am when we're on BST (British Summer Time), although it's sometimes operated on a staggered basis in some areas to avoid everybody's heavy loads coming on at once.
The old "white meter" that some people still refer to was exactly that: A separate meter for the night rate with a white case instead of the standard black. A timer-controlled contactor would apply power to a separate distribution panel to which would be wired the storage heaters. With this system, only loads on that panel were charged at the low rate; everything else remained on the standard meter at all times.
The newer Economy 7 now uses a single meter with multiple rate dials. The PoCo will still supply a contactor so that storage heater loads can be connected to a separate panel, but the entire house is metered at the lower rate overnight.
There is also an Economy 10 tariff now, which gives an extra boost of power to heaters during the afternoon.
